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【期刊论文】Some Homological Invariants of Local PI Algebras
吴泉水, Q.S. Wu, J.J. Zhang
Journal of Algebra 225, 904-935 (2000),-0001,():
-1年11月30日
semilocal PI algebra, Auslander-Buchsbaum formula, depth, local cohomology, Morita duality.,
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【期刊论文】Regularity of involutory PI Hopf algebras
吴泉水, Q.-S. Wu a, and J.J. Zhang b, *,
Journal of Algebra 256 (2002) 599-610,-0001,():
-1年11月30日
Let H be an involutory Hopf algebra over a field of characteristic 0. If H is either a finite module over its affine center or a semiprime noetherian affine PI algebra, then it is Auslander regular and Cohen-Macaulay and is a finite direct sum of prime rings.
Hopf algebra, Global dimension
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【期刊论文】HOMOLOGICAL INTEGRAL OF HOPF ALGEBRAS
吴泉水, D.-M. LU, Q.-S. WU AND J.J. ZHANG
,-0001,():
-1年11月30日
The left and right homological integrals are introduced for a large class of infinite dimensional Hopf algebras. Using the homological integrals we prove a version of Maschke's theorem for infinite dimensional Hopf algebras. The generalization of Maschke's theorem and homological integrals are the keys to study noetherian regular Hopf algebras of Gelfand-Kirillov dimension one.
Hopf algebra,, homological integral,, Gorenstein property,, regularity,, Gelfand-Kirillov dimension,, integral order,, integral quotient,, PI degree.,
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【期刊论文】Homological Identities for Noncommutative Rings
吴泉水, Q.-S. Wu, J.J. Zhang
Journal of Algebra 242, 516-535 (2001),-0001,():
-1年11月30日
The Auslander–Buchsbaum formula and Bass's theorem are proved for a class of nonlocal, noncommutative algebras (including certain affine PI Hopf algebras). We also show that each filtered noetherian affine PI Hopf algebra has finite injective dimension, which partially answers a question of Brown.
Auslander-Buchsbaum formula, Bass', s theorem, AS-Gorensteinness, Hopf algebra.,
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